A technique for the numerical solution of geophysical problems

The theoretical analysis of problems in geophysics, and particularly in seismology, leads in many cases to solutions expressed in terms of integrals that cannot be evaluated by conventional numerical methods. The usual difficulties are connected with the oscillatory nature of the integrand and with the presence of one or more poles in the path of integration. In the simpler problems these difficulties can sometimes be circumvented by appropriate transformations in the complex plane, though this often involves lengthy analysis. A method is presented for the direct and accurate evaluation of such solutions with a minimal use of algebraic manipulations. By way of illustration the method is applied to Lamb's problem with an oscillatory source.